Impact on beer sales of removing the pint serving size: An A-B-A reversal trial in pubs, bars, and restaurants in England

Background Smaller serving sizes could contribute towards reducing alcohol consumption across populations and thereby decrease the risk of 7 cancers and other diseases. To our knowledge, the current study is the first to assess the impact on beer, lager, and cider sales (hereafter, for ease, referred to just as “beer sales”) of removing the largest draught serving size (1 imperial pint) from the options available in licensed premises under real-word conditions. Methods and findings The study was conducted between February and May 2023, in 13 licensed premises in England. It used an A-B-A reversal design, set over 3 consecutive 4-weekly periods with “A” representing the nonintervention periods during which standard serving sizes were served, and “B” representing the intervention period when the largest serving size of draught beer (1 imperial pint (568 ml)) was removed from existing ranges so that the largest size available was two-thirds of a pint. Where two-third pints were not served, the intervention included introducing this serving size in conjunction with removing the pint serving size. The primary outcome was the mean daily volume of all beer sold, including draught, bottles, and cans (in ml), extracted from electronic sales data. Secondary outcomes were mean daily volume of wine sold (ml) and daily revenue (£). Thirteen premises completed the study, 12 of which did so per protocol and were included in the primary analysis. After adjusting for prespecified covariates, the intervention resulted in a mean daily change of −2,769 ml (95% CI [−4,188, −1,578] p < 0.001) or −9.7% (95% CI [−13.5%, −6.1%] in beer sold. The daily volume of wine sold increased during the intervention period by 232 ml (95% CI [13, 487], p = 0.035) or 7.2% (95% CI [0.4%, 14.5%]). Daily revenues decreased by 5.0% (95% CI [9.6%, −0.3%], p = 0.038). Conclusions Removing the largest serving size (the imperial pint) for draught beer reduced the volume of beer sold. Given the potential of this intervention to reduce alcohol consumption, it merits consideration in alcohol control policies. Trial registration ISRCTN.com ISRCTN18365249.


Subject : Sample size calculation [#20221011]
Dear Eleni, You are interested in defining the number of sites required to detect a decrease in beer sales induced by an intervention assuming the same ABA reversal design (set over three 4-weekly periods) as considered in your wine study for all sites, the same effect size as estimated in your wine study.
In this document, we briefly describe the results of the sample size calculation we performed.

/1/ Simulation parameters
On the 10/11/2022, you kindly shared the raw data of your wine study.These data also include daily beer sales, your primary outcome, for which a log normal model mixed model with day of week, (standardised) time, (standardised) revenue and (standardised) temperature as fixed effects, a random intercept and revenue slope per site, site heteroscedastic error terms, i.e., a similar model as the one you chose for the wine study, seemed suitable.
To define the sample size on interest, we performed a simulation-based predictive power analysis [1,2] allowing to incorporate the uncertainty related to the target parameter as estimated in the wine study.We considered -H0 : β1 = 0 versus H1 : β1 < 0, as statistical hypotheses where β1 denotes the intervention fixed effect parameter, a 2.5% type error (often considered for one-sided tests), two estimators, the REML estimator of [3] and the GAMLSS estimator of [4].
We also assumed the same model as described above plus a dichotomous intervention predictor, the same parameters and parameter covariance as estimated on the beer data of your previous study, the same intervention parameter value and uncertainty as estimated on the wine data of your previous study.

/2/ Results
Figure 1 shows the type I error (y-axis) as a function of the number of sites (x-axis) and estimator (coloured lines), as estimated by our Monte Carlo simulation under H0.The horizontal black line corresponds to the α nominal value of 2.5% and the light grey rectangle corresponds to the Monte Carlo simulation error.We can note that the observed type I error of both estimators is slightly greater than the nominal value in most cases, suggesting that significance should be assessed with care when considering a model as complex as the one described in Section 1.  Figure 2 shows the power (y-axis) as a function of the number of sites (x-axis) and estimator (coloured lines), as estimated by our Monte Carlo simulation under H1.We can note that the REML estimator seemingly leads to a greater power while often achieving a better type I error control, the power of the REML is above 0.85 for all considered number of sites.

/3/ Conclusion
The Monte Carlo simulation we considered to assess the operating characteristics of a trial considering the same design and (estimated) effect size as in the wine study, as well as the relationship between the different predictors of interest and your new primary outcome as noted in the your wine study showed that your beer study is already powered at the 85% level with a number of sites as low as 5.
We would suggest to consider a larger number of sites nevertheless due to the model complexity [5].
Let me know if you have questions.

Figure 2 :
Figure 2 : Estimated power (y-axis) as a function of the number of sites (x-axis) and estimator (coloured lines)